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Journal of University of Chinese Academy of Sciences ›› 2021, Vol. 38 ›› Issue (1): 23-28.DOI: 10.7523/j.issn.2095-6134.2021.01.003

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The properties of positive solutions for strongly singular equations with singular potential

TANG Lu, SHUANG Zhen, SUN Yijing   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2019-05-14 Revised:2019-07-04 Online:2021-01-15

Abstract:

We discuss the strongly singular equations of matrix-type,

where Ω is a smooth bounded domain in Rn (n ≥ 3) containing the origin, M(x) is a real symmetric matrix on Ω, -3 < -p < -1, and -n < -μ < 0. We show that all H01-solutions are unbounded when -n < -μ < -1-n/2 and there exists no solution of slow growth when M(x)≡I (identity matrix) and -μ<-2.

Key words: singular potential, strong singularity, real symmetric matrix

CLC Number: